Question

Consider the following hypothesis test:

H ₀:   50

H _a:  > 50

A sample of 70 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05.

a. With  = 52.5, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 2

b. With  = 51, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 4

c. With  = 51.8, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?
SelectYesNo

Answer 1

Solution :

Given that,

Population mean = = 50

Population standard deviation = = 6

Sample size = n = 70

Level of significance = = 0.05

This is a right tailed test.

a)

Sample mean = = 52.5

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.67

The test statistics,

Z =( - )/ (/n)

= ( 52.5 - 50 ) / ( 6 / 70 )

= 3.49

Since it is observed that z = 3.49 > = 1.67 , it is then concluded that the null hypothesis is rejected.

Yes. It is concluded that the population mean is greater than 50.

b)

Sample mean = = 51

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.67

The test statistics,

Z =( - )/ (/n)

= ( 51 - 50 ) / ( 6 / 70 )

= 1.39

Since it is observed that z = 1.39 < = 1.67 , it is then concluded that the null hypothesis is fails to rejected.

No. It is concluded that the population mean is not greater than 50.

c)

Sample mean = = 51.8

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.67

The test statistics,

Z =( - )/ (/n)

= ( 51.8 - 50 ) / ( 6 / 70 )

= 2.51

Since it is observed that z = 2.51 < = 1.67 , it is then concluded that the null hypothesis is fails to rejected.

Yes. It is concluded that the population mean is greater than 50.